A General Theory for Equivalent Barotropic Thin Jets

Abstract

The so-called thin-jet approximation, in which variations along the jet axis are assumed gradual in comparison with variations normal to the axis, allows the calculations of along- and cross-axis structures to be decoupled. The result is a nonlinear equation, with one lesser spatial dimension, governing the meandering of the jet. Here a new such ?path equation? is constructed in the context of a one-layer, reduced-gravity model. The formalism retains two distinct physical processes: a vortex-induction mechanism, originating from the jet curvature, that causes meanders to travel downstream (i.e., usually eastward), and the planetary (beta) effect, induced by meridional displacements, that gives the meanders the allure of Rossby waves and generates a westward (i.e., usually upstream) propagation. After a brief comparison with previous path equations, analytical solutions of the new equation are explored, including solitons and other exact nonlinear wave forms. The presentation concludes with numerical experiments and a brief application to the Gulf Stream.